Exact controllability of a semilinear reaction–diffusion equation governed by a bilinear control

Abstract

This paper investigates the exact controllability of a semilinear reaction–diffusion equation governed by a multiplicative control. Here, the reaction term leads to an unbounded control operator. We will first study the well-posedness and then proceed to the question of exact steering for the system at hand. Our approaches are based on a fixed point argument and the linearization method. The obtained results are further analysed through a numerical example.

Keywords:

• Semilinear parabolic equation
• approximate controllability
• exact controllability
• bilinear control

AMS Classifications:

• 93B03
• 93B05
• 35K57
• 35K58

Disclosure statement

No potential conflict of interest was reported by the author(s).